2020
DOI: 10.1112/mtk.12051
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Combinatorial Inscribability Obstructions for Higher Dimensional Polytopes

Abstract: For 3-dimensional convex polytopes, inscribability is a classical property that is relatively well-understood due to its relation with Delaunay subdivisions of the plane and hyperbolic geometry. In particular, inscribability can be tested in polynomial time, and for every f-vector of 3-polytopes, there exists an inscribable polytope with that f-vector. For higher dimensional polytopes, much less is known. Of course, for any inscribable polytope, all of its lower dimensional faces need to be inscribable, but th… Show more

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Cited by 2 publications
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“…The question which combinatorial types of 3-polytopes are inscribable was raised by Steiner [23] and settled by Steinitz [24] and Rivin [21]. In stark contrast, our understanding of the inscribability problem in dimensions four and up is rather exiguous [20,10]. In [18], we replaced combinatorial equivalence with the discrete-geometric condition of normal equivalence.…”
Section: Introductionmentioning
confidence: 99%
“…The question which combinatorial types of 3-polytopes are inscribable was raised by Steiner [23] and settled by Steinitz [24] and Rivin [21]. In stark contrast, our understanding of the inscribability problem in dimensions four and up is rather exiguous [20,10]. In [18], we replaced combinatorial equivalence with the discrete-geometric condition of normal equivalence.…”
Section: Introductionmentioning
confidence: 99%